Multiply the following complex numbers, marked as blue dots on the graph: $(3 e^{7\pi i / 12}) \cdot (3 e^{13\pi i / 12})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3 e^{7\pi i / 12}$ ) has angle $\frac{7}{12}\pi$ and radius $3$ The second number ( $3 e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius $3$ The radius of the result will be $3 \cdot 3$ , which is $9$ The angle of the result is $\frac{7}{12}\pi + \frac{13}{12}\pi = \frac{5}{3}\pi$ The radius of the result is $9$ and the angle of the result is $\frac{5}{3}\pi$.